trees located on a sloping hillside turn to grow vertically by responding to gravity and and light rays. To measure the height of a tree on a slope it is helpful to know the angle between the tree and the slope ground. If a tree is growing vertically at an angle of 74 degree with respect to the sloped ground and the angle to the top of the tree from a location uphill 110 feet from the base of the tree is 48 degree, how tall is the tree.

Question

mathstudent55 · Answer

Have you tried drawing this?

anonymous · Answer

yup, but its wrong. I have done the calculation base on the wrong graph and got the wrong answer. My teacher says it should be less than 100, but I got like 174ft

mathstudent55 · Answer

Can you show your drawing?
It's a triangle, right?

anonymous · Answer

attachment

mathstudent55 · Answer

Ok, I see it. Let's do a new drawing together following the info in the problem.

mathstudent55 · Answer

Your tree on top of the hill does not make an angle of 74 deg with the hill slope.

mathstudent55 · Answer

|dw:1400790994957:dw|

mathstudent55 · Answer

The tree grows at an angle of 74 deg with the sloped side.

|dw:1400791075219:dw|

mathstudent55 · Answer

Now let's draw the point 110 ft from the base of the tree on the sloped side.

|dw:1400791294078:dw|